I'm not sure the company is owned by the original folks but I started with a Thompson A vise and for a beginner, it really is all you need. It is inexpensive so if you decide you're not interested, you won't be out much $$$. (80 bucks)

If you do decide to go street rat crazy and become a frequent fly tyer, you'll need to step up to a more expensive, pedestal style rotary vise. Until then, this is a good starter vise.

I've been using a Cabela's Super II vise for 25 years. Mine came with two extra jaws (I just changed them for the first time!) full 360 rotating and the price today is still $20!! I don't think Cabela's offers the extra jaws anymore but other shops and catalogs still do for $20. I tie #22 midges to #5/0 Deceivers with the same jaws. Unless you have a great presentation fly room or have more money than you know what to do with...a vise is made to hold a hook, the fish don't care what kind of vise you have--spend your fish money on a vintage Hardy reel and a bamboo rod!!

I started tying about a year ago. My wife bought me a kit that included this vise. It holds the hook, and generally works fine. If I had been buying for myself I would have gone one step higher to something like a Danvise. Watching Youtube vides of EP wrapping flies with his rotary vise has made me want to try a rotary.
It's a Sunrise AA. About $20. Other companies make them for even less $$.

I'd recommend starting by taking a fly tying class at a fly shop if you can. That will let you use one or more potential vices you might be interested in buying during the class. Even if they have only one model, you will learn what you like about some versions. Most shops will let you tie a bit on the vices they have for sale so you can find the one that suits your style and price range. Most of us go through several vices during a tying career certain that the newest one will be the last, and if you get six of us in a room together, we will most likely disagree what the best vice is.

Two things I love about the Danvise are it's low initial cost and the fact that it is all black matte finish. I have tied on some of those high end art objects that are all polished and bright and didn't like them a bit. I have never heard anyone else complain about the reflection off of those things but to me it is a distraction.

I tied for decades on a Thompson Model A. It worked just fine. If you eventually decide you really like tying, you could always upgrade....but it won't be necessary to do so. Exquisitely crafted flies can be tied on very simple vises....no vise, regardless of its features, contributes all that much to a fly's creation, compared to the tyer's experience and skill. All a vise really has to do is hold the hook securely.